Infrared spectroscopy of diatomic molecules - a fractional calculus approach

TL;DR

This paper introduces a fractional calculus approach to the quantum harmonic oscillator, enabling a smooth transition between vibrational and rotational spectra, which aids in analyzing infrared spectra of diatomic molecules.

Contribution

It presents a novel fractional Schrödinger equation method to model diatomic molecule spectra, bridging vibrational and rotational behaviors.

Findings

Fractional approach models IR spectra effectively.

Smooth transition between vibrational and rotational spectra.

Numerical solutions of fractional Schrödinger equation obtained.

Abstract

The eigenvalue spectrum of the fractional quantum harmonic oscillator is calculated numerically solving the fractional Schr\"odinger equation based on the Riemann and Caputo definition of a fractional derivative. The fractional approach allows a smooth transition between vibrational and rotational type spectra, which is shown to be an appropriate tool to analyze IR spectra of diatomic molecules.